University of Ljubljana Institute of Mathematics, Physics and Mechanics Department of Mathematics Jadranska 19, 1 111 Ljubljana, Slovenia Preprint series, Vol. 44 (2006), 1005 CIRCULAR COLOURING THE PLANE Matt Devos Javad Ebrahimi Mohammad Ghebleh Luis Goddyn , Bojan Mohar Reza Naserasr ISSN 1318-4865 July 5, 2006 Ljubljana, July 5, 2006